Assign, close and reopen chats
Hand a chat to a teammate, take one yourself, close it when it is done, and pick it up again later.
Assigning a chat tells your team who is looking after it, so two people never answer the same visitor.
Assign a chat
At the top of a conversation, the list next to Close shows who it is assigned to. Choose a teammate, or yourself (marked (me)). Choose Unassigned to put it back for anyone to take.
You do not have to assign chats by hand: the first teammate to reply takes the chat.

Above the list, Mine shows the chats assigned to you, and Unassigned the ones nobody has taken.
Close a chat
When the visitor's question is answered, click Close. The conversation moves to Closed, and the visitor's chat window says "This conversation was closed. Send a message to start a new one."
If the visitor writes again later, a new conversation starts in Open.
Reopen a chat
Click Closed above the list, open the conversation and click Reopen. It goes back to Open with everything that was said, and you can reply as before.